2025/03/05 by Khabibullin, B. N.
#30D30 #30D35 (Primary) 30D20 #31A05 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.03296
We solve the following three problems. 1. How much can the radial growth of an entire function f be reduced by multiplying it by some nonzero entire function? We give the answer in terms of the growth of the integral means of ln|f| over the circles centered at the origin. 2. We estimate the smallest possible radial growth of non zero entire functions that vanish on a given distribution of points Z. We solve this problem in terms of the growth of the radial integral counting function of Z. 3. Let F=f/g be a meromorphic function with representations as the ratio of entire functions f≠ 0 and g≠ 0. How small can the radial growth of entire functions f and g be in such representations in relation to the growth of the Nevanlinna characteristic of F? All solutions have a non-asymptotic uniform character, and the obtained inequalities are sharp. All of them are based on some main theorem for subharmonic functions, which relies on the Govorov--Petrenko--Dahlberg--Essén inequality and uses our general results on the existence of subharmonic minorants.